Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival modeling, and reliability theory. However, there do not currently exist valid tests for whether the underlying density of given data is log-concave. The recent universal inference methodology provides a valid test. The universal test relies on maximum likelihood estimation (MLE), and efficient methods already exist for finding the log-concave MLE. This yields the first test of log-concavity that is provably valid in finite samples in any dimension, for which we also establish asymptotic consistency results. Empirically, we find that the highest power is obtained by using random projections to convert the d-dimensional testing problem into many one-dimensional problems, leading to a simple procedure that is statistically and computationally efficient.
翻译:形状限制在数据分布模型的完全非对称和完全参数分析方法之间产生灵活的中间点。对日志精确度的具体假设是由跨经济学、生存模型和可靠性理论的应用驱动的。然而,目前尚没有关于特定数据的潜在密度是否为日志精确度的有效测试。最近的通用推论方法提供了一个有效的测试。通用测试依靠最大可能性估计,而找到日志对流 MLE的有效方法已经存在。这产生了在任何层面的有限样本中都可明显有效的对日志精确度的首次测试,我们为此也建立了无损一致性结果。我们偶然地发现,通过随机预测将二维测试问题转化为许多一维问题,从而导致一个统计性和计算效率的简单程序。